Feeds:
Posts
So here’s something I’ve been thinking about. Given a simple connected graph $G$, define $\rho(G)$ to be its largest positive eigenvalue; in other words, if $w_n$ counts the number of walks (equivalently, closed walks) of length $n$ on $G$, then
$\displaystyle \rho(G) = \limsup_{n \to \infty} \sqrt[n]{w_n}.$